How do you find the distance between point A(-3, 5) and point B(4, -6) in the coordinate plane?

3 Answers
Jun 10, 2015

Answer:

#d(A,B)=sqrt(170)~~13.03#.

Explanation:

Having the points #A(-3,5) and B(4,-6)# on the same plane.
We calculate the distance d with the formula:
#d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#.
So in this case we have:
#d=sqrt((4-(-3))^2+(-6-5)^2)=sqrt(49+121)=sqrt(170)~~13.03#

Jun 10, 2015

Answer:

You first work out the #x#- and #y#-distances and then use Pythagoras

Explanation:

In the horizontal (x) direction the distance is:
#Deltax=4-(-3)=7#
In the vertical (y) direction the distance is:
#Deltay=-6-5=-11# or just plain #11#
(you should draw this on coordinate paper)

We now have a right-sided triangle, where the hypotenuse is the distance between A and B.

So #(AB)^2=(Deltax)^2+(Deltay)^2->#
#(AB)^2=7^2+11^2=49+121=170->#
#AB=sqrt170~~13.0#

Jun 10, 2015

Answer:

Find distance between A (-3, 5) and B (4, -6)

Explanation:

Use formula for distance: #d^2 = (x2 - x1)^2 + (y2 - y1)^2#

#d^2 = (4 + 3)^2 + (-6 - 5)^2 = 49 + 121 = 170#

d = 13.04